Mass flow sensors are used in a wide variety of applications to measure the mass flow rate of a gas or other fluid. One application in which a mass flow sensor may be used is a mass flow controller. In a conventional mass flow controller, the mass flow rate of a fluid flowing in a main flow path is regulated or controlled based upon a mass flow rate of a portion of the fluid that is diverted into a typically smaller conduit forming a part of the mass flow sensor. Assuming laminar flow in both the main flow path and the conduit of the sensor, the mass flow rate of the fluid flowing in the main flow path can be determined (and regulated or controlled) based upon the mass flow rate of the fluid flowing through the conduit of the sensor.
A flow sensor, in general, refers to any device or combination of devices that responds to fluid flow by providing an output indicative of the fluid flow rate. A thermal mass flow sensor refers to a flow sensor that provides an output that varies with the flow rate of a fluid in a flow path based on heat convection, conduction and/or flux resulting from the flow of the fluid. The term “fluid” is used herein to describe any type of matter in any state that is capable of flow. It is to be understood that the term fluid applies to liquids, gases, and slurries comprising any combination of matter or substance capable of flow.
One conventional thermal mass flow sensor is illustrated in FIG. 1. Thermal mass flow sensor 10 includes a conduit 12 having an upstream resistance coil 14 and a downstream resistance coil 16 wound about the conduit 12 at a predetermined spacing such that the conduit has a characteristic length related to the length l. The upstream and downstream coils are coupled to sensor electronic circuit 18. Typically, coils 14 and 16 are of the variety wherein the resistance of the coil is a function of temperature. When no fluid is flowing through conduit 12, the sensor is in a balanced state. For example, coils 14 and 16 may comprise one leg of respective Wheatstone bridge configurations such that the balanced state may be achieved by having electronic circuit 18 drive upstream coil 14 and downstream coil 16 to the same temperature. When both coils are at the same temperature their resistances are equal such that the voltage drop across each resistor is also equal (i.e., V1 is equal to V2). Electronic circuit 18 may be configured to detect differences between voltage V1 and V2 and output the difference as a voltage signal 20, referred to as the sensor output signal or simply the sensor output.
As fluid flows through the conduit, the fluid transfers heat from the upstream coil 14 toward the downstream coil 16 according to properties of heat convection. As a result, the temperature of the downstream coil 16 becomes greater than that of the upstream coil 14, thereby varying the respective resistances and unbalancing the sensor electronic circuit 18. The voltage drop V2 will no longer equal the voltage drop V1 and sensor electronic circuit 18 will detect the difference in voltage drops and output the difference as the sensor output signal 20. The amount of heat transferred by convection, and thus the sensor output, is proportional to the mass flow rate of the fluid.
It should be appreciated that a sensor output need not be a voltage signal but may be any of various other signals and may depend upon the design of the flow sensor. For example, a sensor output may be a voltage signal as illustrated in FIG. 1, a current signal, a digital or analog signal or any other signal capable of indicating fluid flow through a conduit of the sensor.
Many applications, for example, semiconductor fabrication processes, may require that a particular flow sensor operate with a variety of different fluids and/or combinations of fluids. In practice, providing such a flow sensor is a difficult task. For example, the sensor output of conventional thermal mass flow sensors may depend both on the mass flow rate of the fluid in the flow path and, in part, on the type of fluid. That is, the thermal and/or physical characteristics of a fluid in the flow path may affect how the sensor output voltage changes with flow rate.
FIG. 2 illustrates sensor response curves for eight different types of fluid. A sensor response curve refers generally to any representation based on sensor output as a function of or in association with flow rate. In FIG. 2, the horizontal axis represents the actual fluid flow rate of the respective fluid through the flow path. The vertical axis represents the normalized sensor output voltage resulting from the fluid flow rate. The normalized sensor output voltage is the sensor output voltage divided by the sensor output voltage resulting when a fluid is flowing at its maximum flow rate through the flow path, referred to as full scale flow. That is, the vertical axis represents the fraction of the full scale sensor output voltage.
Ideally, each sensor response curve would be a linear function of flow rate. However, in practice it can be seen that the sensor response curves have varying degrees of curvature and that the curvature itself may be a fluid dependent function of flow rate. Conventionally, it is not well understood how the sensor response curves vary from fluid to fluid. This unpredictability makes it difficult to develop a flow sensor that responds satisfactorily to a range of fluids over an adequate range of flow rates. More particularly, it is difficult to provide a flow sensor that operates satisfactorily with an arbitrary fluid over an adequate range of flow rates.